Purpose: We consider the fractionation problem in intensity-modulated proton therapy (IMPT). It is known that a low α/β ratio in the normal tissue favors a hyperfractionated regimen. In contrast, a low α/β ratio in the tumor gives rise to hypofractionation. However, in current clinical practice, the patient is treated with the same dose distribution in each fraction. We demonstrate that the standard biologically equivalent dose (BED) model gives rise to non-uniform fractionation schemes, i.e. for an intermediate range of α/β ratios, it can be optimal to deliver distinct dose distributions in different fractions.

Methods: We consider the simultaneous optimization of IMPT dose distributions and the fractionation scheme. This is achieved by simultaneously optimizing multiple (possibly distinct) IMPT plans for different fractions. To that end, we consider an objective function based on the cumulative BED distribution delivered over all fractions.

Results: It is shown that the optimal treatment regimen may consist of distinct IMPT plans. For proton therapy this has an intuitive explanation: The dose in the entrance region of the proton beam is mostly independent of the range. Thus, an incident proton beam can primarily irradiate the distal part of the tumor in one fraction, and the proximal part in the subsequent fraction - without significantly changing the dose in the normal tissue. This can be interpreted as the possibility of hypofractionating subregions of the tumor while continuing to hyperfractionate in the normal tissue.

Conclusion: To date, the determination of the fractionation scheme and the optimization of the spatial dose distribution in IMRT and IMPT are considered independently. Here, we demonstrate that both problems are interdependent. In particular, the therapeutic ratio can potentially be improved by delivering distinct dose distributions in different fractions.